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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 2576i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2576.a1 | 2576i1 | \([0, 0, 0, -8419, -301667]\) | \(-4124632486295808/70140333767\) | \(-1122245340272\) | \([]\) | \(5376\) | \(1.1107\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2576i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2576i do not have complex multiplication.Modular form 2576.2.a.i
sage: E.q_eigenform(10)